Answer:
62.2
Step-by-step explanation:
Hello There!
we need to find the missing angle using law of cosines
The law of cosines formula for finding an angle is
[tex]cosC=\frac{a^2+b^2-c^2}{2ab}[/tex]
Important note: c^2 = opposite side of missing angle
so we are given all of the measurements so all we need to do is plug in the values
[tex]cosX=\frac{19^2+30^2-27^2}{2(19)(30)} \\19^2=361\\30^2=900\\27^2=729\\\\900+361-1261\\1261-729=532\\2(19)(30)=1140\\\frac{532}{1140} =.4666666667\\cosX=.4666666667[/tex]
so our last step would be to isolate the variable (x)
to do so we take the inverse of cos -^1(arccos) and multiply that by each side
[tex]X=arccos(.4666666667)\\X=62.18186071[/tex]
then we would round to the nearest tenth and get that x = 62.2
